Day 21 Sinusoidal Analysisc

We started the day with talking about impedance and admittance. V = ZI, V/I = jwL, V/I = 1/jwC.
We then wrote it down on the white board.

White board work of finding Z. Z = R + jX

We then move onto an example to do.

White board work we used 10 cos4t. First we found the phasor domain of the circuit. and then used i = vs/Z

White board continued. i = Vs/Zc and Vc = IZc.

White board work we had to multiply top and bottom with the conjugate of bottom to get the numbers right.

We then move onto another example.

White board work, used Zc = 1/jwC, -j = -90 degrees.

We then move onto the lab of the day: Impedance
Prelab: White board work of the prelab for phasor for each Vr and V(t). Plus other information.

White board work of the prelab.

White board work of pre lab with circuits drawn and values.

White board work of more prelab and other stuff.

Following pictures of the lab, data and white board at the end.

Picture of the signals with data at bottom. period is 1ms. Vin 1.5V, Vout .5 V.

Picture of data for 1khz signal, Vin = 1.37, Vout = 600 mV. Period  = 1ms.

Clearer picture of the one above.

Clear picture with R = 100 ohms, same data as above.

Clear picture then before same data for 1khz signal. Period 100 us.

Picture of Vin and Vout for 1khz, R = 100.

Picture for 10 khz.

Picture of data at 10 khz, Vin = 1.3V Vout = 570 mV. Period = 100us

Picture with capacitor at 1khz.

Picture with capacitor added C1 = .47uf

Picture same as above for data.

Picture of data at 1khz for Capacitor. Vin = 1.5V Vout = 535 mV. Period 1ms.

Picture at 5kz for C1.

Picture of the signals for 5 khz capacitor. Period 1.6 ms.

Picture of data same signal as above.

Picture of data at 5khz capacitor. Vin  = 1.45 V, Vout = 156 mV. Period is 200 us.

Picture of capacitor at 10khz.

Picture of signal at 10khz for capacitor.

Picture of data of same signal as above.

Picture of data of signal at 10khz for capacitor. Vin = 1.5 V, Vout = 116 mV. Period 100 us.

Picture of 1khz inductor. L = 1m H.

Picture of signal of 1khz inductor.

Picture of data same picture as above.

Picture of data of 1khz inductor. Vin = 1.5 V, Vout = 250 mV. Period = 1 ms.

Picture of 5khz inductor.

Picture of 5khz signal of the inductor.

Picture of data same as above.

Picture of data for 5khz signal of inductor. Vin = 1.4 V, Vout  = 927 mV. Period 200 us.

Picture of 10khz of inductor.

Picture of the 10khz signal for inductor.

Picture of data same as above.

Picture of data for 10khz inductor. Vin  = 1.4 V, Vout = 1 V. Period 100us

Picture of the inductor circuit.

Picture of the inductor circuit. Edgar does great wiring.

White board work of post lab stuff and calculations.

White board work of post lab work and calculations.

More post lab white board work.

White board work continued for lab.

Octave work that Jon did for us. Fancy and efficient work!

Picture of the Octav work for the three circuits with having in order R = 100, and then current and then Voltage. This would be our tabulate for post lab.

In conclusion of the lab we saw the Vout differ for each different frequencies. The period also change with frequency. Depending on the type of circuit for the Capacitor circuit the change of frequency cause the voltage to drop for each increase of frequency and the period to change to 100, 200, and back 100 us for 1k, 5k, and 10khz respectively. For the Inductor circuit the change of frequency case the voltage to increase and the period to change to drop from 1ms, 200us to 100us for each change respectively. The calculations were done by Jon and all are correct.

Lastly we did example of combining Z impedance.
We worked an example.

White board work of example. First transform everything to phasor domain. Do parallel Zc||Zl and then add R. Then voltage division. Lastly back to time domain.

White board work of changing to phasor domain and back to time domain.

Lastly we talked about phase shifters.

White board work of the example.

In summary we started the day with impedance. We had examples of how to change capacitors and inductors to the phasor domain. We then did a long lab for three frequency and see how the R,L,C circuits behave with different frequency. We learned that for C circuits frequency increase caused Vout to drop and the inverse is true for L circuits. For R it didn't matter. Lastly we talked about phase shifter and how they can be useful.

Day 20 Sinusoids and Phasors (NO LAB)

We started the day with talking about phasors and sinusiods. We went with f = 1/T and w = 2pif. Our white board work below shows an example done in class with the right transformations.

White board work of a sin wave of V(t). It is shifted up .03 with an amp of .17

White board work continued with a clear picture of the interpretation of V(t).

White board work of the equation of the sine wave.

We then talked about the phasor graph and did an example below.

White board work of the phasors on the graph.

More detalied explantion for phasor where C  = sqrt(X^2 + y^2) and the phase angel tan-1(y/x),
x = rcosphi and y = rsinphi. We can switch from REKT to polar and use REKT for +- and Polar for multiplication and division.

White board work of stuff stated above.

We then move onto an example to try. We first transformed phasor to time domain and then added the relative components together and then back to phasor.

White board work of the transformation of phasor to time domain for addition then back to phasor for answer.

More white board work continued with the phasor answer taken to negative 1 power.

White board work continued with the -1 of the phasor which we get to be .02 @ -45.

We move onto examples of going time domain to phasor for many problems.

White board work of many examples of time domains to phasors. If sine add -90 to it. If negative sine add 90.

We then move onto the more examples.

White board work of V =  j8e-j20.

More white board work of examples of phasors and time domain. It was important to use the magnitude by taking the sqrt( real^2 + fake^2) and then the tan-1(fake/real) for angle.

White board work that used importation information named above and then translated back to time domain.

More white board work.

White board work with the angles and mags drawn.

Another example to try with real numbers and components.

White board work with real components and numbers we found L = .1H V = 1/L di/dt, i = integral of v. V = 12 cos(60t+45) and finally then do the phasor transformation and then back to time domain, we subs 90 since it was sin.

Last part of the day we talked about our E44 projects. Mine is here drawn out with beautiful pictures and notes. It will be the best fly killer by laser ever.

Beautiful picture of penmanship and artistically ability used to convey a wonderful idea of having less flies in the world.

In summary there was no lab today. We spent the whole day talking about phasors and time domain and did a lot of examples. Some notes to take are that if it is sine sub 90 from phi, if sine is negative add 90. If it is cosine leave alone. Rect is for addition and subtraction and polar is for multiplication and division. Lastly talked about my project "Fly Killer, by lazer".

Day 19 2nd Order Circuits Contb

We started with talking about the Qi wireless charger which had two modes of charging, Resonant and Inductive. There is a trade off between each mode, loosely coupled system trade off larger distance at the cost of lower power transfer efficiency and higher EMF. Tightly coupled system produce less heat which is favorable for heat budgeted devices like cell phones.

We then move onto the real gritty stuff of continued the work on Series and Parallel RLC. We started with the step respond of a series RLC circuit. It is a second order differential, with i = Cdv/dt. Vt = Vn + Vf. In natural response Vs = 0. Vn can be OD,CD,UD, Vf = Vinf = Vs.
 OD = A1e^s1t+A2e^s2t
 CD = (A1+A2t)e^-alpha*t
 UD = (A1coswdt + A2sinwdt)e^-alpha*t
The complete version then is:
 OD = Vs + A1e^s1t+A2e^s2t
 CD = Vs + (A1+A2t)e^-alpha*t
 UD = Vs + (A1coswdt + A2sinwdt)e^-alpha*t

A1 and A2 are from V(0) and dV(0)/dt. V is Cap, I is current of inductor.

Knowing this we try an example.

White board work: Using above information and numbers given.

More white board work continued.

White board work: more white board work we found di/dt in terms of A2 = -10. S = j8

More white board work continued.

White board work continued, found A1 = 20V used wd since it was a O

We then move onto the step response of a parallel RLC circuit. We use current for parallel.
I(t) = In + If. . In can be OD,CD,UD, If = Is.
 OD =Is +  A1e^s1t+A2e^s2t
 CD = Is + (A1+A2t)e^-alpha*t
 UD = Is + (A1coswdt + A2sinwdt)e^-alpha*t
We tried an example of our own with the knowledge attain above.

White board work: S1 = -1+j S2 = -1-j, UD. If = Is  = 5A

More white board work continued.

White board worked continued: A2 = -5

We then move onto the lab of the day: RLC circuit response.
Prelab: We first did the lab in every-circuit. Then we wrote the second order diff on the white board. Then estimated damp ratio. And lastly rise time and frequency on white board.

Picture of the everycircuit schematic and working, min -20 mV max 62.3 mV and freq 1khz

White board work of prelab it has the second order diff, (kind of cut off but is there).

White board work of the second order.

More white board prelab work.

White board work: Has alot of information has Vo at 42mV. A1 = 42. alpha = 500, w0 = 10,000, UD. Damping ratio = .05.

Picture of the time respond in the every-circuit app.

Picture of the time respond of every-circuit, 10 ms.

Picture of real circuit.

Picture of the real circuit, none of that fake stuff.

Picture of the real stuff data.

Picture of the step respond.

More picture data.

Picture of data of step respond freq 200 hz, Vin = 40 mV Vout = 2 volts. Matches every-circuit and our white board work very closely with Vin 42 mV. As percent diff  it is = 4.7 % error.

More pictures of real, cleaner version!

Picture of the real but prettier thanks to Edgar. We will not name the original maker.

White board work for POST lab:
We found wd to be 9987, r1 real to be 47.4 ohms. A1 - 42, A2 = 6.3

White board work showing the used second order diff and the steps needed to find A1 and A2.

More white board work, found di/dt and t of rise time = 10us. Which matched was close to every-circuit but was off by a factor of 10 to get percent error of = 1000%. We think we lost a exponent somewhere in our math but think we got it correctly.

In conclusion of the lab: We found our numbers to match every-circuit and the data from diligent. We are off by a factor 100 since picture data says 1us and we got 10us and every-circuit says 10ms. We are close but far away. Our percent error for A1 and A2 are good with Vin being 42 mV and recorded at 40 mV our percent error is 4.7%. The damping ratio is .05 and we got .5 again out numbers are off by a factor so somewhere in the math we lost an exponent but our percent error would be 0 but in this case it is over 1000%. We also think we may be off because real has non-ideal components while every-circuit had ideal components.

The text file for this contiues on with talking general second order circuts like op amps and smoothing digital signals but I dont have pictures for that.

In summary of the day we learned more about step response circuit and did a lab on it and briefly talked about second order op amps. We learned that series use V for step response and parallel use I for step response but the equations of OD,CD, UD are the same for both just need to swamp out V for I. Vf = Vinf, If = Iinf.